Abstract
Many tasks in computer vision suffer from missing values in tensor data, i.e., multi-way data array. The recently proposed tensor tubal nuclear norm (TNN) has shown superiority in imputing missing values in 3D visual data, like color images and videos. However, by interpreting in a circulant way, TNN only exploits tube (often carrying temporal/channel information) redundancy in a circulant way while preserving the row and column (often carrying spatial information) relationship. In this paper, a new tensor norm named the triple tubal nuclear norm (TriTNN) is proposed to simultaneously exploit tube, row and column redundancy in a circulant way by using a weighted sum of three TNNs. Thus, more spatial-temporal information can be mined. Further, a TriTNN-based tensor completion model with an ADMM solver is developed. Experiments on color images, videos and LiDAR datasets show the superiority of the proposed TriTNN against state-of-the-art nuclear norm-based tensor norms.
Highlights
In recent decades, the rapid progress in multi-linear algebra [1] has provided a firm theoretical foundation for many applications in computer vision [2], data mining [3], machine learning [4], signal processing [5], and many other areas
triple tubal nuclear norm (TriTNN) and Tubal-Alt-Min are: (a) TriTNN preserves the low-rank structure by summing three tubal nuclear norms, whereas Tubal-Alt-Min adopts low-rank tensor factorization to characterize the low-rank property of a tensor. They are two different kinds of models for tensor completion (b) Since TriTNN is based on the tubal nuclear norm, it is formulated as a convex optimization problem (21)
To explore the effectiveness of the proposed TriTNN-based model, we compare with the following nuclear norm-based tensor completion models:
Summary
The rapid progress in multi-linear algebra [1] has provided a firm theoretical foundation for many applications in computer vision [2], data mining [3], machine learning [4], signal processing [5], and many other areas. In many computer vision tasks, the data, like color images or videos, may be moderately redundant, it can be interpreted by fewer latent factors [11]. In many computer vision applications, like image or video inpainting, one has to tackle the missing values in the observed data tensor due to many circumstances [2,16], including failure of sensors, errors or loss in communication, occlusions or noise in the environment, etc. It is Algorithms 2018, 11, 94; doi:10.3390/a11070094 www.mdpi.com/journal/algorithms
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